I had the same problem with my iPod Touch 5th generation. After moving through recommendations by others (reset iPod, reinstall iTunes...), it still wasn't syncing. I could access my entire library as long as I was hooked into iTunes either directly or through wi-fi.
On a whim, I went into Settings on my iPod, then to Music. If you have an iCloud account, the default setting of the iCloud Music Library is "on". I switched it off and sure enough, the music in my library (stored on my laptop) began downloading! Yay!
I am not a technician but it strikes me that the default setup directs the iPod to search the iCloud first but then it goes no further. If the iCloud Music Library is disabled, the iPod then goes to the next available inventory...the music stored on the system.
Hope this helps - I know it's an incredibly frustrating situation! 😕